PRP Records

Probable Primes Top 10000

(277054 PRPs in the top)


What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!


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1-250   251-500   501-750   751-1000   1001-1250   1251-1500   1501-1750   1751-2000   
2001-2250   2251-2500   2501-2750   2751-3000   3001-3250   3251-3500   3501-3750   3751-4000   
4001-4250   4251-4500   4501-4750   4751-5000   5001-5250   5251-5500   5501-5750   5751-6000   
6001-6250   6251-6500   6501-6750   6751-7000   7001-7250   7251-7500   7501-7750   7751-8000   
8001-8250   8251-8500   8501-8750   8751-9000   9001-9250   9251-9500   9501-9750   9751-10000   


Rank Probable prime Digits (> 50000) Who ? When ?
9751(8116^18397-1)/811571917Serge Batalov08/2020
975210^71910+2511971911Patrick De Geest05/2016
975310^71910-80171910Robert Price04/2016
9754(2^238862+1230)/271905Stefano Morozzi01/2020
9755(2^238864+3198)/271905Stefano Morozzi01/2020
97562^238845-11265171900Enzo Doria06/2014
97572^238792-11124571884Enzo Doria05/2014
97586*7^85059+571884Lelio R Paula10/2014
975919312^5273+5273^1931271881Hans Havermann11/2019
976019176^5603+5603^1917671880Hans Havermann11/2019
97612^238752-11058971872Enzo Doria05/2014
9762(2^238739+2738)/271868Stefano Morozzi01/2020
976312^66581+771853Lelio R Paula07/2014
9764(7*2^238691+1)/4122971850Lelio R Paula06/2012
97654*3^150568-571840Lelio R Paula04/2014
97666^92301+6771825Lelio R Paula01/2015
97672^238568+9876533171817Jason Earls01/2009
97682^238541-11272371808Enzo Doria06/2014
97692^238529-1594971805Enzo Doria04/2013
97709*5^102721-871800Lelio R Paula10/2014
97712^238494-16571794Lelio R Paula02/2012
977218035^9562+9562^1803571790Hans Havermann10/2019
977318390^7993+7993^1839071771Hans Havermann11/2019
97742^238389-11090571763Enzo Doria05/2014
9775(145*10^71760-1)/971762Serge Batalov12/2014
97767^84913+506271760Mike Oakes02/2010
977721218^2409+2409^2121871756Hans Havermann10/2019
9778(F(11446)^31-F(11445)^31)/F(11444)71753Wayne Halsdorf03/2012
9779(1227^23227-1)/122671742Serge Batalov08/2020
97802^238268-9730571726Lelio R Paula05/2012
9781gcd(V(1330365),5*F(266073)*(F(266073)-1)+1)71724Serge Batalov04/2015
9782(2^238249+3770)/271720Stefano Morozzi01/2020
97832^238235-11324771716Enzo Doria07/2014
97842*12^66450-5^6645071712Mike Oakes11/2010
9785(2^238213+lucasV(1,2,238213)+1)/471709Mike Oakes11/2016
97862^238199-11181771706Enzo Doria05/2014
9787lucasU(46,1,43125)+lucasU(46,1,43124)71696Mike Oakes04/2009
97882^238144+9876533171689Jason Earls01/2009
9789(2^238137+2810)/271687Stefano Morozzi01/2020
979018^57102-426571679Enzo Doria03/2013
9791(73*10^71670-1)/971671Robert Price01/2015
97922^238081+1155*23808171670Henri Lifchitz02/2005
97932^238067-11192571666Enzo Doria05/2014
9794(2^238024+3690)/271653Stefano Morozzi01/2020
9795(7388^18523-1)/738771653Serge Batalov08/2020
979619143^5528+5528^1914371644Hans Havermann10/2019
979765401!4+12871638Robert Price09/2019
979836^46030+3571637Norbert Schneider04/2014
9799(74*10^71621+313)/971622Robert Price11/2017
98002^237905-9171617Lelio R Paula02/2012
9801(31*2^237902-1)/12371616Lelio R Paula01/2014
9802(15185*2^237866-1)/4396771605Lelio R Paula04/2015
980316696^16957+16957^1669671603Norbert Schneider09/2019
9804(24737*2^237841+1)/2571601Lelio R Paula06/2014
98052^237846+129971599Lelio R Paula05/2012
98066^92004+19980171594Mike Oakes02/2011
9807159^32516+271581Lelio R Paula05/2013
98082^237781+85571580Lelio R Paula05/2012
9809(2^237754+814)/271571Stefano Morozzi01/2020
98102^237720-407971561Yves Minet06/2011
98112^237698-11094571555Enzo Doria05/2014
98122^237695-11323971554Enzo Doria07/2014
98138*5^102362-971549Lelio R Paula10/2014
9814(4*10^71546-31)/971546Erik Branger05/2011
98152^237650+3771540Lelio R Paula02/2012
981618^56977-439171522Enzo Doria03/2013
9818(22699*2^237565+1)/413663771512Lelio R Paula06/2014
9817((1+sqrt(7)+sqrt(6))^48479-1)*((1+sqrt(7)-sqrt(6))^48479-1)*((1-sqrt(7)+sqrt(6))^48479-1)*((1-sqrt(771512Mike Oakes05/2009
9819(26*10^71503+7)/371504Erik Branger11/2013
9820(4*10^71498+173)/371499Robert Price01/2017
98213^149848+11071496Lelio R Paula11/2014
98222^237498+51371495Lelio R Paula05/2012
98232^237485+10771491Lelio R Paula02/2012
9824(2^237465+9)/241971481Lelio R Paula05/2012
98252^237439-11223771477Enzo Doria06/2014
9826(2^237427+2510)/271473Stefano Morozzi01/2020
98272^237407-978771467Lelio R Paula11/2009
98282^237383+7295371460Enzo Doria04/2016
982919768^4119+4119^1976871458Hans Havermann11/2019
983082^37337-81^3733771457Robert Price01/2015
9831(1017*2^237313-1)/1971441Lelio R Paula04/2015
98322^237311+19171438Lelio R Paula02/2012
983311699^17560+17560^1169971437Norbert Schneider09/2019
9834(25188^16231-1)/2518771432Serge Batalov08/2020
98352^237280-5971429Lelio R Paula02/2012
9836(2^237275+1038)/271427Stefano Morozzi01/2020
9837(2^237265+2774)/271424Stefano Morozzi01/2020
983811^68564-9871403Lelio R Paula01/2015
98392^237173+7480171397Enzo Doria04/2016
9840(2^237150+1458)/271389Stefano Morozzi01/2020
984115^60697+5671386Lelio R Paula01/2015
98422^237118+17771380Lelio R Paula02/2012
98432^237110+6971378Lelio R Paula02/2012
984415^60690-5871377Lelio R Paula01/2015
9845(5*2^237125-1)/59985119171374Lelio R Paula01/2014
984620311^3262+3262^2031171363Hans Havermann11/2019
9847(3^149567+2)/53971359Lelio R Paula06/2012
9848(5*10^71357-143)/371358Robert Price04/2016
98492^237039-11462171356Enzo Doria05/2015
9850(2^237037+3462)/271355Stefano Morozzi01/2020
985112^66116-3771352Lelio R Paula02/2015
9852(3^149497+2^149497)/571328Jean-Louis Charton10/2010
98532^236941-6694571327Lelio R Paula05/2012
98542^236911-114771318Yves Minet10/2009
985565^39337+4271315Lelio R Paula01/2016
9856(13319^17291-1)/1331871313Serge Batalov08/2020
9857(2^236863+3234)/271303Stefano Morozzi01/2020
98586*10^71299+771300Dmitry Domanov11/2010
9859(25*2^236843+1)/375371295Lelio R Paula06/2012
986010^71291+1518771292Patrick De Geest03/2016
986210^71291-558730911971291Robert Price03/2015
986110^71291-27358171291Patrick De Geest03/2016
9863-numer(bernoulli(22808)/22808)71290T. D. Noe09/2005
9864(2^236781+1514)/271278Stefano Morozzi01/2020
9865(2^236775+2886)/271277Stefano Morozzi01/2020
986615105^17054+17054^1510571271Norbert Schneider08/2018
9867(2^236738+9)/1371265Lelio R Paula05/2012
98685^101949+4271260Lelio R Paula07/2014
9869(9811^17851-1)/981071253Serge Batalov08/2020
98707*10^71238-3971239Robert Price07/2020
98715*10^71237+971238Dmitry Domanov11/2010
98722^236634-1602571234Enzo Doria04/2013
987371^38478+7071233Norbert Schneider12/2014
98749*7^84280+871226Lelio R Paula10/2014
9875(2^236603+2378)/271225Stefano Morozzi01/2020
9876(10^71223+59)/371223Serge Batalov12/2014
987723260^1153+1153^2326071219Hans Havermann10/2019
9878(15185*2^236569-1)/45371216Lelio R Paula04/2015
987951829#+(216091#)/(51829#)71208Makoto Morimoto03/2016
98802^236528-17371203Lelio R Paula02/2012
98813*2^236511-571198Lelio R Paula04/2014
98822^236477-9971187Lelio R Paula02/2012
988311^68356-213071186Enzo Doria12/2012
988415128^17031+17031^1512871186Norbert Schneider08/2018
988511^68355-312071185Enzo Doria12/2012
9886(2^236463+998)/271183Stefano Morozzi01/2020
988736^45737-35^4573771181Robert Price10/2012
9888(3^149183-lucasV(1,3,149183)+1)/371178Paul Vanderveen12/2017
98892^236432+2571174Lelio R Paula02/2012
98905^101818-1280671168Enzo Doria02/2013
9891(7*10^71166-457)/971166Robert Price09/2017
989265^39253+6271163Lelio R Paula01/2016
989339^44718+3871150Norbert Schneider05/2014
989418996^5557+5557^1899671137Hans Havermann10/2019
989564983!4-25671135Robert Price11/2019
98962^236296-40771133Yves Minet02/2012
98972^236286-11771130Lelio R Paula02/2012
9898(2^236283+1074)/271128Stefano Morozzi01/2020
98992^236257-11119371121Enzo Doria05/2014
99007^84149-3671115Lelio R Paula08/2014
9902164176#-p(164176)71108Henri Lifchitz12/2018
9901(2^236214+2934)/271108Stefano Morozzi01/2020
99032^236209-11212371106Enzo Doria06/2014
990418^56644-498571104Enzo Doria03/2013
9905(46*10^71077+521)/971078Robert Price08/2017
990621^53753+271074Ray Chandler08/2011
9907(5482^19009-1)/548171070Serge Batalov08/2020
9908(86*10^71068-311)/971069Robert Price10/2017
99092^236081-11092371068Enzo Doria05/2014
9910(293*27^49642-1736)/1371058Curtis Bright05/2015
991165^39192+2271052Lelio R Paula01/2016
9912(2^236016+1246)/271048Stefano Morozzi01/2020
9913(439#+1)^397-439#^39771038Mike Oakes11/2010
99147^84050-271031Lelio R Paula09/2013
991515813^16916+16916^1581371031Norbert Schneider09/2019
9916(2^235956+3978)/271030Stefano Morozzi01/2020
9917(3568^19993-1)/356771021Serge Batalov08/2020
991864877!4+12871007Robert Price09/2019
991918562^6681+6681^1856270997Hans Havermann10/2019
9920(2^235802+474)/270984Stefano Morozzi01/2020
992120^54558-2370982Lelio R Paula01/2015
99222^235793-11255570981Enzo Doria06/2014
992349936!3-3^4993670981Robert Price08/2015
99242^235787-7879570979Lelio R Paula05/2012
9925(2^235761+2930)/270971Stefano Morozzi01/2020
9926Perrin(581132)70970Eric W. Weisstein02/2011
9927(2^235748+3478)/270967Stefano Morozzi01/2020
992814^61913-9770961Lelio R Paula01/2015
99302^235720+1632170959Yves Minet03/2010
99292^235718+1609570959Lelio R Paula05/2012
9931163841#+34993370957Nicolas PALAU11/2016
99322^235710+770956Lelio R Paula02/2012
9933(175^31627+1)/17670939Eric Chen10/2017
9934(2^235644+670)/270936Stefano Morozzi01/2020
99352^235635-11208770934Enzo Doria06/2014
9936153^32467+15270931Norbert Schneider11/2018
99382^235575-196570916Lelio R Paula05/2012
99376^91133+10170916Lelio R Paula01/2015
9939(24755^16141-1)/2475470914Serge Batalov08/2020
9940(1102^23311-1)/110170914Serge Batalov08/2020
9941(21181*2^235505+1)/370898Lelio R Paula06/2014
9942(14*10^70896+211)/970897Robert Price11/2017
99435^101425+8470894Lelio R Paula07/2014
9944177^31536+270893Lelio R Paula05/2013
994543*71^38292+470891Serge Batalov03/2016
9946(29*2^235506-1)/11202978570888Lelio R Paula01/2014
994711^68045-153070862Enzo Doria12/2012
9948(6969^18439-1)/696870861Serge Batalov08/2020
99495*10^70858+2170859Robert Price01/2017
99512^235326+370841Donovan Johnson02/2006
995034523!2+470841Robert Price02/2015
9952(31*2^235307+1)/370836Lelio R Paula06/2012
9953(2^235310+1038)/270836Stefano Morozzi01/2020
99542^235308+13570835Lelio R Paula02/2012
9955r(35414,90)*1000+91170831Patrick De Geest07/2004
99562^235274+15970825Lelio R Paula02/2012
99573^148409+7070810Lelio R Paula11/2014
9958(19*10^70794+17)/970795Robert Price03/2015
9959(2^235144+1350)/270786Stefano Morozzi01/2020
99602^235108-23270970775Paul Bourdelais03/2013
996122995^1196+1196^2299570773Hans Havermann11/2019
9962(2^235099-2^117550+1)/57077211/2006
996319^55325-670748Lelio R Paula08/2014
9964257^29356+29356^25770746Norbert Schneider10/2014
996522*10^70729+370731Robert Price10/2017
99662^234956+1171570729Lelio R Paula05/2012
9967(7*10^70727-43)/970727Robert Price10/2014
9968(2^234897+3906)/270711Stefano Morozzi01/2020
99692^234890-3034170709Enzo Doria11/2012
997017^57461+1470703Lelio R Paula01/2015
997118281^7366+7366^1828170697Hans Havermann09/2019
9972(9179*2^234834-1)/570696Lelio R Paula04/2015
99732*10^70688+5170689Robert Price10/2017
9974123^33822-12270685Norbert Schneider01/2015
99757*10^70680-9970681Robert Price11/2017
9976(2^234784+3646)/270677Stefano Morozzi01/2020
9977(21*2^234772-1)/209570672Lelio R Paula01/2014
9978(2^234762+1498)/270671Stefano Morozzi01/2020
9979(24355^16111-1)/2435470668Serge Batalov08/2020
9980(2^234723+3690)/270659Stefano Morozzi01/2020
9981(2^234718+3798)/270657Stefano Morozzi01/2020
9982(2^234680+2902)/270646Stefano Morozzi01/2020
9983(29*2^234686-1)/2114570645Lelio R Paula01/2014
9984(15*2^234688-1)/527814170643Lelio R Paula01/2014
99862^234655-6770639Lelio R Paula02/2012
9985(79*10^70638-61)/970639Robert Price10/2015
99872^234652-17370638Lelio R Paula02/2012
99882^234618-364570628Lelio R Paula05/2012
9989(2^234610-5)/1970624Lelio R Paula05/2012
99904*5^101038+970624Lelio R Paula10/2014
99912^234603+7196370623Enzo Doria04/2016
99922^234600-11312970622Enzo Doria07/2014
9993(2^234601+1446)/270622Stefano Morozzi01/2020
99942^234586+970618Lelio R Paula02/2012
99953^148008+2670618Robert Price11/2013
9996(7*10^70616-151)/970616Robert Price09/2017
999765^38947+3270608Lelio R Paula01/2016
9998(2^234517+2750)/270597Stefano Morozzi01/2020
999918363^6988+6988^1836370594Hans Havermann10/2019
10000(2^234488-3)/1170587Lelio R Paula05/2012


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Created by  Henri Lifchitz & Renaud Lifchitz : October, 26 2000, last modification: January, 25 2021 11:23 (Time in France)

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